08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
71 lines
5.3 KiB
Text
71 lines
5.3 KiB
Text
elimTest0 : forall (motive : Nat -> Sort.{u_1}) (x : Nat), (forall (y : Nat), motive y) -> (motive x)
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def elimTest0.{u_1} : (motive : Nat → Sort u_1) → (x : Nat) → ((y : Nat) → motive y) → motive x :=
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fun motive x h_1 => h_1 x
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elimTest1 : forall (α : Type.{u_1}) (β : Type.{u_2}) (motive : (List.{u_1} α) -> (List.{u_2} β) -> Sort.{u_3}) (x : List.{u_1} α) (y : List.{u_2} β), (Unit -> (motive (List.nil.{u_1} α) (List.nil.{u_2} β))) -> (forall (a : α) (as : List.{u_1} α) (b : β) (bs : List.{u_2} β), motive (List.cons.{u_1} α a as) (List.cons.{u_2} β b bs)) -> (forall (a : α) (as : List.{u_1} α), motive (List.cons.{u_1} α a as) (List.nil.{u_2} β)) -> (forall (b : β) (bs : List.{u_2} β), motive (List.nil.{u_1} α) (List.cons.{u_2} β b bs)) -> (motive x y)
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def elimTest1.{u_1, u_2, u_3} : (α : Type u_1) →
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(β : Type u_2) →
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(motive : List α → List β → Sort u_3) →
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(x : List α) →
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(y : List β) →
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(Unit → motive [] []) →
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((a : α) → (as : List α) → (b : β) → (bs : List β) → motive (a :: as) (b :: bs)) →
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((a : α) → (as : List α) → motive (a :: as) []) →
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((b : β) → (bs : List β) → motive [] (b :: bs)) → motive x y :=
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fun α β motive x y h_1 h_2 h_3 h_4 =>
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List.casesOn x (List.casesOn y (h_1 ()) fun head tail => h_4 head tail) fun head tail =>
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List.casesOn y (h_3 head tail) fun head_1 tail_1 => h_2 head tail head_1 tail_1
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elimTest2 : forall (α : Type.{u_1}) (motive : forall (n : Nat), (Vec.{u_1} α n) -> (Vec.{u_1} α n) -> Sort.{u_2}) (n : Nat) (xs : Vec.{u_1} α n) (ys : Vec.{u_1} α n), (Unit -> (motive ([mdata _inaccessible:1 OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)]) (Vec.nil.{u_1} α) (Vec.nil.{u_1} α))) -> (forall (n : Nat) (x : α) (xs : Vec.{u_1} α n) (y : α) (ys : Vec.{u_1} α n), motive ([mdata _inaccessible:1 HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))]) (Vec.cons.{u_1} α n x xs) (Vec.cons.{u_1} α n y ys)) -> (motive n xs ys)
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def elimTest2.{u_1, u_2} : (α : Type u_1) →
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(motive : (n : Nat) → Vec α n → Vec α n → Sort u_2) →
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(n : Nat) →
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(xs ys : Vec α n) →
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(Unit → motive 0 Vec.nil Vec.nil) →
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((n : Nat) →
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(x : α) → (xs : Vec α n) → (y : α) → (ys : Vec α n) → motive (n + 1) (Vec.cons x xs) (Vec.cons y ys)) →
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motive n xs ys :=
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fun α motive n xs ys h_1 h_2 =>
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(fun xs_1 =>
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Vec.casesOn (motive := fun a x => n = a → xs ≍ x → motive n xs ys) xs_1
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(fun h =>
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Eq.ndrec (motive := fun n => (xs ys : Vec α n) → xs ≍ Vec.nil → motive n xs ys)
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(fun xs ys h =>
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⋯ ▸
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Vec.casesOn (motive := fun a x => 0 = a → ys ≍ x → motive 0 Vec.nil ys) ys (fun h h_3 => ⋯ ▸ h_1 ())
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(fun {n} a a_1 h => False.elim ⋯) ⋯ ⋯)
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⋯ xs ys)
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fun {n_1} a a_1 h =>
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Eq.ndrec (motive := fun n => (xs ys : Vec α n) → xs ≍ Vec.cons a a_1 → motive n xs ys)
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(fun xs ys h =>
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⋯ ▸
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Vec.casesOn (motive := fun a_2 x => n_1 + 1 = a_2 → ys ≍ x → motive (n_1 + 1) (Vec.cons a a_1) ys) ys
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(fun h => False.elim ⋯)
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(fun {n} a_2 a_3 h =>
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n_1.elimOffset n 1 h fun x =>
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Eq.ndrec (motive := fun {n} =>
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(a_4 : Vec α n) → ys ≍ Vec.cons a_2 a_4 → motive (n_1 + 1) (Vec.cons a a_1) ys)
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(fun a_4 h => ⋯ ▸ h_2 n_1 a a_1 a_2 a_4) x a_3)
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⋯ ⋯)
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⋯ xs ys)
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xs ⋯ ⋯
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elimTest3 : forall (α : Type.{u_1}) (β : Type.{u_2}) (motive : (List.{u_1} α) -> (List.{u_2} β) -> Sort.{u_3}) (x : List.{u_1} α) (y : List.{u_2} β), (Unit -> (motive (List.nil.{u_1} α) (List.nil.{u_2} β))) -> (forall (a : α) (b : β), motive (List.cons.{u_1} α a (List.nil.{u_1} α)) (List.cons.{u_2} β b (List.nil.{u_2} β))) -> (forall (a₁ : α) (a₂ : α) (as : List.{u_1} α) (b₁ : β) (b₂ : β) (bs : List.{u_2} β), motive (List.cons.{u_1} α a₁ (List.cons.{u_1} α a₂ as)) (List.cons.{u_2} β b₁ (List.cons.{u_2} β b₂ bs))) -> (forall (as : List.{u_1} α) (bs : List.{u_2} β), motive as bs) -> (motive x y)
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def elimTest3.{u_1, u_2, u_3} : (α : Type u_1) →
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(β : Type u_2) →
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(motive : List α → List β → Sort u_3) →
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(x : List α) →
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(y : List β) →
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(Unit → motive [] []) →
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((a : α) → (b : β) → motive [a] [b]) →
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((a₁ a₂ : α) → (as : List α) → (b₁ b₂ : β) → (bs : List β) → motive (a₁ :: a₂ :: as) (b₁ :: b₂ :: bs)) →
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((as : List α) → (bs : List β) → motive as bs) → motive x y :=
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fun α β motive x y h_1 h_2 h_3 h_4 =>
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List.casesOn x (_sparseCasesOn_112 y (h_1 ()) fun h => h_4 [] y) fun head tail =>
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List.casesOn tail
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(_sparseCasesOn_113 y
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(fun head_1 tail => _sparseCasesOn_112 tail (h_2 head head_1) fun h => h_4 [head] (head_1 :: tail)) fun h =>
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h_4 [head] y)
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fun head_1 tail =>
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_sparseCasesOn_113 y
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(fun head_2 tail_1 =>
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_sparseCasesOn_113 tail_1 (fun head_3 tail_2 => h_3 head head_1 tail head_2 head_3 tail_2) fun h =>
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h_4 (head :: head_1 :: tail) (head_2 :: tail_1))
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fun h => h_4 (head :: head_1 :: tail) y
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